70 calories of heat are required to raise the temperature of 2 mole of an ideal gas at constant pressure from $30^\circ$ C to $35^\circ$ C. The amount of heat required to raise the temperature of the same gas through the same range at constant volume is

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50 calories It is given that 70 calories of heat are required to raise the temperature of 2 mole of an ideal gas at constant pressure from $30^\circ$ C to $35^\circ$ C. Also, specific heat at constant pressure, `"C"_"P" = (triangle Q)/(ntriangleT) => "C"_"P" = 70/ (2 xx (35-30) => "C"_"P" =70/(2 xx 5) => "C"_"P" = 7 "calories" -" mol" ^-1K^-1` For an ideal gas , CP - CV = R = 8.314 J - mol -1 K-1 ≃ 2 calories mol-1K-1 $\Rightarrow$ CV =CP -R $\Rightarrow$ CV = (7-2) calories - mol-1 K-1 $\Rightarrow$ CV = 5 calories - mol-1 K-1 $\Rightarrow$ CV = `(triangle "Q")/(ntriangle"T") => 5 = (triangle "Q")/(2 xx (35-30)` $\Rightarrow$ Δ Q = 5 $\times$ 2 $\times$ (35-30) $\Rightarrow$ Δ Q = 5 $\times$ 2 $\times$ 5 $\Rightarrow$ Δ Q = 50 calories Therefore, 50 calories need to be supplied to raise the temperature of 2 moles of gas from 30-35 oC at constant volume.

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