One mole of an ideal gas requires $207\ J$ heat to raise the temperature by $10\ K$ when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same $10\ K,$ the heat required is (Given the gas constant $R = 8.3\ J/mol - K$)

Question

Dr. Abubacker · Accepted Answer

(d) $(\mathrm{\Delta}Q)_{P} = \mu C_{P}\mathrm{\Delta}T \Rightarrow 207 = 1 	imes C_{P} 	imes 10$
$\Rightarrow C_{P} = 20.7\frac{Joule}{mol - K}.\ Also\ C_{P} - C_{V} = R$
$\Rightarrow C_{V} = C_{P} - R = 20.7 - 8.3 = 12.4\frac{Joule}{mole - K}$
So, $(\mathrm{\Delta}Q)_{V} = \mu C_{V}\mathrm{\Delta}T = 1 	imes 12.4 	imes 10 = 124\ J$

Q. One mole of an ideal gas requires $207\ J$ heat to raise the temperature by $10\ K$ when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by the same $10\ K,$ the heat required is (Given the gas constant $R = 8.3\ J/mol - K$)

Explanation

Reviewed by Dr. Abubacker

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