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# Specific Heat

Specific heat is the amount of heat per unit mass required to raise the temperature by one degree Celsius. The relationship between heat and temperature change can be seen below. However this relationship does not apply is a phase change occurs because the heat added or removed during a phase change does not change the temperature.

Q = cmÎ”T

Where Q is the heat added, c is the specific heat, m is mass, and Î”T is the change in temperature.

The specfic heat of water is 1 calorie/gram oC = 4.186 joule/gram oC. This is higher than any other common substance. As a result, water plays a very important role in temperature regulation. The specific heat per gram of water is higher than that for a metal.

The molar specific heat of most solids at room temperature and above is nearly constant. This comes from the Law of Dulong and Petit. At lower temperatures the specific heat drops as quantum processes become significant. The low temperature behavior is described by Einstein-Debye model of specific heat.

## BrainMass Categories within Specific Heat

### Enthalpy

Solutions: 5

Enthalpy is the measure of the total amount of energy in a system.

### Phase Changes

Solutions: 17

A phase change is the transformation of a substance from one state to another.

### Thermal Equilibrium

Solutions: 6

Thermal equilibrium is the relationship between two respective physical bodies.

### Entropy change: Water

5.2 Calculate the entropy change for each of the following: (a) 10g of steam at l00Â°C and a pressure of one atmosphere condensing into water at the same temperature and pressure. (The latent heat of vaporization of water is 22571 Jg^-1). (b) 10g of water at l00Â°C and a pressure of one atmosphere cooling to 0Â°C at the same

### Simplify Representations of the Diesel Cycles

A simplified representation of the diesel cycle, with just air as the working substance. Show that the efficiency of the engine is: n = 1 - 1/y((1/rye-1/ryc)/(1/re-1/rc)) where re = V3/V2, the expansion ratio, and rc = V3/V1, the compression ratio. If re = 5, rc = 15 and y = 1.4, evaluate n. Notice that the compression r

### Physics - Calorimetry Problem

Suppose you took a 22.68-gram chunk of metal and heated it to 95.8 oC. Then you put it in 41.04 grams of water at 24.9 oC and the system reached a final temperature of 38.1 oC. Calculate the specific heat of the metal, assuming a perfectly insulated container.

### Boiling Liquid Nitrogen

Liquid nitrogen boils at a chilly -195.8 degrees celsius when the pressure is one atmosphere. A silver coin of mass 1.5 x 10^-2 kg and temperature 25 degrees celsius is dropped into the boiling liquid. What mass of nitrogen boils off as the coin cools to -195.8 degrees celsius?

### Water Frozen to Ice

If an aluminum sphere has a mass of 23.01 grams at 60.0 Celsius and lowered into a cup containing 20.00 mL of water at 21.0 Celsius. The final temperature of the water and the sphere was 44.0 Celsius assuming no heat was loss calculate the mass of water that is frozen into ice?

### The Mass of Boiling Liquid Nitrogen

Liquid Nitrogen has a boiling point of -195.8 celsius. Drop a silver coin with a mass 10 kg in it. The initial temperature of coin is 90 degrees. Find what mass of the liquid nitrogen boils off as nitrogen cools?

### Temperature Change and Joules of Energy

2. A 2kg copper pot contains 8 kg of water. Both are initially at 20Â°C. If heat is added so that the temperature is now 80Â°C, determine the amount of heat is put into each material; the copper and the water. 3. If we have 500ml of water, how many joules of energy will be required to change the temperature from 25Â°C to 95Â°

### recovery time for heat

The recovery time of a hot water heater is the time required to heat all the water in the unit to the desired temperature. Suppse that a 52 gallon ( 1.00 gal=3.79 x 10^-3 m^3) unit starts with cold water at 11 degrees Celsius and delivers hot water at 53 degrees Celsius. The unit is electric and utilizes a resistance heater (

### Laboratory Problem

This is a problem we did in lab that dealt with measuring specific heat. Please provide answers along with solutions to the following questions. These problems mainly deal with specific heat capacity. See attached file for full problem description. A. What is the energy gained by water? Include measurement uncertainty?

### Wave Length of Sound

What is the wavelength of a 2,000-kHz sound wave (a) in air, (B) in helium, and (c) in water?

### Method of Mixtures

See the attached file. Method of Mixtures: C1 = specific heat of mass one (m1) C2 = specific heat of mass two (m2) Thot = temperature of hot mass Tcold = temperature of cold mass Tf = final temperature of the mixture Using the following equation, show the final equation needed to solve for each variable: C1 m1 (Tf - T

### Show the final equation needed to solve for each variable

Specific Heat: C = specific heat Q = amount of heat m = mass Î”t = temperature change Using the following equation, show the final equation needed to solve for each variable: Q = Cm Î”t Solve for: C = m = Î”t =

### Latent heat and energy during a phase transition

A 50.0 gram ice cube at -2 oC is heated until all of it is turned to steam at 100.0 oC. How much energy in calories was added to do this?

### A problem based on gas laws

A balloon is filled with Helium gas at 20 degrees C and 1.0 atm of pressure. (1 atm = 1.01 x 10^5 Pa). After filling, the balloon's volume is 8.50 m^3. The helium is then heated until it reaches a final temperature of 55 degrees C. The balloon expands at a constant pressure during this process. What is the heat lost or gain

### Density, Pressure and Temperature

1. Spy balloon is to be constructed of a material with a mass of 0.5kg. it will be filled with helium and must be able to carry and instrument payload of 50kg at an altitude of 1000m where the density of the air is 1.16 kg/m^3. what mass of helium will be required. 2. If the temperature of gas (measured in K) is doubled a-

### Phase Change - Latent Heat - Specific Heat: Ice to Steam

How much energy is required to change a 40-g ice cube from ice at -10 degrees C to steam at 110 degrees C?

### Hot iron horseshoe

A hot iron horseshoe (mass = 0.340 kg) which has just been forged, is dropped into 1.71 L of water in a 0.310 kg iron pot initially at 19.3oC. If the final equilibrium temperature is 24.8oC, calculate the initial temperature of the hot horseshoe (in Celsius).

### Calculating the specific heat of a gas at a constant pressure

The specific heat of a gas at a constant pressure is 1.70 times the specific heat at a constant volume. Find the specific heat at a constant pressure. Universal gas constant= r= 8.31 J(mol K)

### How Snow Can Contain More Heat Than Water

Explain how it is possible for a 30,000 kg of snow at 0 deg C to contain more heat energy than 1 mL of liquid water at 100 deg C. (Assume a pressure of one atmosphere).

### Solve: Specific Heat

Question: The specific heat of a gas at constant pressure is 1.70 times the specific heat at constant volume. Find the specific heat at constant pressure (universal gas constant R= 8.31j/(mol k). a. 12.5j/mol k b. 24.0 j/mol k c. 18.0 j/mol k d. 20.2 j/mol k

### Thermodynamics: ice water

An ice cube weighs 30 grams at 0 degrees Celsius. It is added to 200 g of water at 80 degrees Celsius in an insulated container. What is the final temperature of the mixture? The affect of the container is negligible.

### Heat explained in this answer

How much heat is added to 500g of water to raise its temperature from 15 degrees C to 85 degrees C? a. 35 j b. 1.5 * 10^8j c. 1.5 * 10^5j d. 3.5 * 10^4j

### Speed of sound, Bulk modulus of a gas

1) The bulk modulus of a gas varies with pressure. In the case of the air, the bulk modulus of air is equal to 1.40 times its pressure. the atmospheric pressure at sea level is 1.01 * 105 N/m2. The density of air at sea level is 1.20 kg/m3. For these conditions, what is the speed of sound as it passes through the air? a.328 m

### Thermodynamics: Isochoric Process

A 2-kW baseboard electric resistance heater in a vacant room is turned on and kept on for 15 min. The mass of the air in the room is 75 kg, and the room is tightly sealed so that no air can leak in or out. The temperature rise of air at the end of 15 min is:

### Thermodynamics: Isochoric Change

A well-sealed room contains 80 kg of air at 200 k Pa and 25Â°C. Now solar energy enters the room at an average rate of 1 kJ/s while a 100-W fan is turned on to circulate the air in the room. If heat transfer through the walls is negligible, the air temperature in the room in 30 min will be:

### Calculate Specific Heat of Solid Phase and of Liquid Phase

An experiment measures the temperature of a 500 g substance while steadily supplying heat to it. The figure shows the results of the experiment (see attachment) What is the (a) specific heat of the solid phase, (b) specific heat of the liquid phase?

### Rise in temperature after dropping a water filled balloon

A tourist drops a 1-liter water-filled balloon from the top of a monument (170m high). If air resistance is negligible and almost all the motion energy heats the water, find the increase in temperature of the water when it hits the pavement. (hint: equate mgh in joules to the quantity of heat mc (change) T and express c, the

### Specific heat capacity

Question: A piece of glass has a temperature of 85.4C. Liquid that has a temperature of 43.0C is poured over the glass, completely covering it, and the temperature at equilibrium is 51.4C. The mass of the glass and the liquid is the same. Ignoring the container that holds the glass and liquid and assuming that the heat lost to

### Specific/Heat Capacity - Extensive or Intensive Quality?

The heat capacity is defined as the amount of energy required to change the temperature of an object. The specific heat capacity is defined as the amount of energy required to change the temperature of an object per mole of the substance. a) Heat capacity is an Intensive quantity Extensive quantity b) Specific h

### Quantum statistics

Consider a 2-level system with an energy splitting between the upper and lower level. Using Boltzmann statistics, show that the heat capacity of the 2-level system equals: (see attachment for equation) What happens in the limit of (see attachment for equation)