1. Tardigrade
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  3. Physics
  4. 70 calories of heat are required to raise the temperature of 2 moles of an ideal gas at constant pressure from 30°C to 35°C.The amount of heat required to raise the temperature of the same sample of the gas through the same range at constant volume is (Gas constant = 1.99 cal/K-mole)

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Q. 70 calories of heat are required to raise the temperature of 2 moles 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 sample of the gas through the same range at constant volume is (Gas constant = 1.99 cal/K-mole)

AIIMSAIIMS 2014

Solution:

As dQ = CPm$\Delta$T
\Rightarrow 70 = CP \times; 2(35 - 30)
\Rightarrow CP = 7 cal/mole/$^{\circ}$C
$\quad$$\quad$CV = CP - R
$\quad$$\quad$$\quad$= 7 - 1.99 = 5.01 cal mol-1 $^{\circ}$C-1
∴ dQ$^{'}$ = CVm$\Delta$T
$\quad$ $\quad$ = 5.01 $\times$ 2 $\times$ (35 - 30) = 50.1 cal