JEE Main & Advanced Physics Kinetic Theory of Gases Sample Paper Topic Test - Kinetic Theory of Gases

  • question_answer
    40 calories of heat is needed to raise the temperature of 1 mol of an ideal monoatomic gas from \[20{}^\circ C\] to \[30{}^\circ C\] at a constant pressure. The amount of heat required to raise its temperature over the same interval at a constant volume (R = 2 cal/mol/K) is

    A) 20 cal

    B) 40 cal

    C) 60 cal

    D) 80 cal

    Correct Answer: A

    Solution :

    [a] At constant pressure
                \[{{(\Delta Q)}_{p}}=\mu {{C}_{p}}\Delta T=1\times {{C}_{p}}\times (30-20)=40\]
                \[\Rightarrow \]            \[{{C}_{p}}=4\frac{\text{calorie}}{\text{moke}\,\text{kelvvin}}\]
                \[\therefore \]    \[{{C}_{v}}={{C}_{p}}-R=4-2=2\,\frac{\text{calorie}}{\text{mole }\!\!\times\!\!\text{ kelvin}}\]
                Now,    \[{{(\Delta Q)}_{v}}=\mu {{C}_{v}}\,\Delta T\]
                            \[=1\times 2\times (30-20)\]
                            \[=20\,\,\text{cal}\]


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