50 , cal of heat is required to raise the tem | vedclass

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(C) Given: Heat at constant pressure $Q_P = 50 \, cal$,number of moles $n = 1 \, mol$,change in temperature $\Delta T = 25^{\circ} C - 20^{\circ} C =

Vedclass · Accepted Answer

$40$

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(C) Given: Heat at constant pressure $Q_P = 50 \, cal$,number of moles $n = 1 \, mol$,change in temperature $\Delta T = 25^{\circ} C - 20^{\circ} C = 5 \, K$,and gas constant $R = 2 \, cal / mol \cdot K$.First,we calculate the molar heat capacity at constant pressure $(C_P)$:$Q_P = n C_P \Delta T$$50 = 1 	imes C_P 	imes 5$$C_P = 10 \, cal / mol \cdot K$.Using Mayer's relation,$C_P - C_V = R$,we find the molar heat capacity at constant volume $(C_V)$:$C_V = C_P - R$$C_V = 10 - 2 = 8 \, cal / mol \cdot K$.Now,calculate the heat required at constant volume $(Q_V)$:$Q_V = n C_V \Delta T$$Q_V = 1 	imes 8 	imes 5 = 40 \, cal$.Therefore,the correct option is $C$.

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