Question bank/JEE Main/Physics

A diatomic ideal gas is heated at constant volume until the
pressure is doubled and again heated at constant pressure until volume
is doubled. Find out the average molar heat capacity for whole process.
in K)
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rd ml nqxuk ugha gks

A28.5B23.5C25.3D23.5

Show answer and solution▾

Let initial pressure, volume, temperature be P_0, V_0, T_0
indicated by state A in P-V diagram. The gas is then isochorically taken
to state B (2P_0, V_0, 2T_0) and then taken from state B to state C
(2P_0, V_0, 4T_0) isobarically
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fd uhps P-V fp=k bls fQj levk;rfud izfØ B (2P_0, V_0,
2T_0) vkSj fQj Bls C (2P_0, V_0, 4T_0) (2P_0, V_0, 4T_0) rd
[IMAGE] Total heat absorbed by 1 mole of gas (by definition of molar heat
capacity)
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$\Delta Q = C_{v}\left( 2T_{0} - T_{0} \right) + C_{p}\left( 4T_{0} - 2T_{0} \right)$
$= \frac{5}{2}RT_{0} + \frac{7}{2}R \times 2T_{0} = \frac{19}{2}{RT}_{0}$
Total change in temperature from state A to C is
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$\Delta T = 3T_{0}$
Molar heat capacityeksyj m"ek

Source: Grass-G / Ph-26 Physics paper 1 15 Jan.docx