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70 cal of heat is required to raise the temperature of 2 moles of an ideal gas at constant pressure from $30^{0} C$ to $35^{0} C$ . What is the amount of heat required to raise the temperature of same gas through the same range at constant volume? ( $R = 2 c a l / m o l e / K$ )

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28 J

Zero

50 cal

75 J

answer is B.

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Detailed Solution

For Isobaric process,

$Q = {nC}_{p} dT$ , Here Q=70 cal, n=2 , dT=5.

$\Rightarrow C_{p} = 7 cal$

$C_{V} = C_{P} - R = 7 - 2 = 5 cal / mole / K$

So, Heat required under constant volume is given by

$Q = {nC}_{v} dT = 2 \times 5 \times 5 = 50 cal$

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