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    Heat absorbed by monoatomic ideal gas

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    How much heat is needed to heat one mole of an ideal monatomic gas from 100K to 500 K at constant volume?

    choices in answers are

    a. 5kJ b. 8kJ c. 49J d. 82kJ

    © BrainMass Inc. brainmass.com December 24, 2021, 5:05 pm ad1c9bdddf
    https://brainmass.com/physics/first-law-of-thermodynamics/heat-absorbed-monoatomic-ideal-gas-27523

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    The first law of thermodynamics is an energy conservation law.
    It states that the heat added to the system minus the work done by the system must result in a change in the internal energy of the system.

    Or in formula:

    Note: in this formulation, work done by the system (in this case the gas) is a positive number. Work done on the system is negative.

    Now, work of against pressure is:

    Where V is the volume and P is the external pressure.

    You could see that there are two cases where the work is zero: the gas expands against vacuum (P=0), or that the volume is constant (dV=0)

    So in our case the work done by the system is zero (constant volume).

    Therefore we are left with:

    Which means that all the heat added to the system is converted into internal energy (which manifests itself as increased temperature).

    The internal energy of monoatomic ideal gas at any given temperature is given by the state equation:

    Where n is the number of moles, R= is the ideal gas constant and T is the temperature.

    Thus:

    And since we have:

    Note that the difference between two temperatures in Celsius is the same as the difference in Kelvins.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 5:05 pm ad1c9bdddf>
    https://brainmass.com/physics/first-law-of-thermodynamics/heat-absorbed-monoatomic-ideal-gas-27523

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