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(B) For a monatomic gas,the adiabatic index is $\gamma = 5/3$.At constant pressure,the heat supplied is given by $\Delta Q_P = n C_P \Delta T = 20 \,

Vedclass · Accepted Answer

$12$

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(B) For a monatomic gas,the adiabatic index is $\gamma = 5/3$.At constant pressure,the heat supplied is given by $\Delta Q_P = n C_P \Delta T = 20 \, J$.At constant volume,the heat supplied is given by $\Delta Q_V = n C_V \Delta T$.We know that $C_P = \gamma C_V$,so $C_V = C_P / \gamma$.Substituting this into the equation for constant volume:$\Delta Q_V = n (C_P / \gamma) \Delta T = \frac{1}{\gamma} (n C_P \Delta T)$.Substituting the given values:$\Delta Q_V = \frac{1}{5/3} 	imes 20 = \frac{3}{5} 	imes 20 = 12 \, J$.

$A$ certain amount of an ideal monatomic gas needs $20 \, J$ of heat energy to raise its temperature by $10^{\circ} C$ at constant pressure. The heat needed for the same temperature rise at constant volume will be ........ $J$.

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