Four moles of a perfect gas heated to increase its temperature by $2^{\circ} C$ absorbs heat of 40 cal at constant volume. If the same gas is heated at constant pressure the amount of heat supplied is (R $=$ 2 cal/mol K)

28 cal

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56 cal

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84 cal

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94 cal

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Solution

The correct option is B 56 cal
Heat supplied at constant volume
$Q_{v} = n C_{v} △ T$
$40 = 4 \times C_{v} \times 2$
$C_{v} = 5$ cal/mol.K
$C_{p} = C_{v} + R = 5 + 2 = 7 c a l / m o l . k$
$\Rightarrow$ Heat supplied at constant pressure
$Q_{p} = n C_{p} △ T = 4 \times 7 \times 2$
$Q_{p} = 56 c a l$

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Four moles of a perfect gas heated to increase its temperature by 2∘C absorbs heat of 40 cal at constant volume. If the same gas is heated at constant pressure the amount of heat supplied is (R= 2 cal/mol K)

The correct option is B 56 calHeat supplied at constant volumeQv=nCv△T40=4×Cv×2Cv=5 cal/mol.KCp=Cv+R=5+2=7cal/mol.k⇒ Heat supplied at constant pressureQp=nCp△T=4×7×2Qp=56cal

Four moles of a perfect gas heated to increase its temperature by $2^{\circ} C$ absorbs heat of 40 cal at constant volume. If the same gas is heated at constant pressure the amount of heat supplied is (R $=$ 2 cal/mol K)