SATHEE: Heat and Thermodynamics 4 Question 5

Heat and Thermodynamics 4 Question 5

5. A cylinder with fixed capacity of $67.2 L$ contains helium gas at STP. The amount of heat needed to raise the temperature of the gas by $20^{\circ} C$ is

[Take, $R = 8.31 J m o l^{- 1} K^{- 1}$ ]

(2019 Main, 10 April I)

(a) $700 J$

(b) $748 J$

(d) $350 J$

Show Answer

Solution:

Given, capacity of cylinder is $= 67.2 L$ and $Δ T = 20^{\circ} C$

At STP volume $= 22.4 L$

$∴$ Number of moles $= \frac{67.2}{22.4} = 3$

Now, change in heat is given as

$Δ Q = n C_{V} Δ T$

Substituting the given values, we get

$\begin{aligned} Δ Q & = 3 \times \frac{3 R}{2} \times 20 (∵ for He gas, C_{V} = \frac{3}{2} R) \\ = 90 R J \end{aligned}$

Given, $R = 8.31 J m o l^{- 1} K^{- 1}$

$∴ Δ Q = 90 \times 8.31 = 747.9 J = 748 J$

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Heat and Thermodynamics 4 Question 5

5. A cylinder with fixed capacity of 67.2L contains helium gas at STP. The amount of heat needed to raise the temperature of the gas by 20∘C is

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5. A cylinder with fixed capacity of $67.2 L$ contains helium gas at STP. The amount of heat needed to raise the temperature of the gas by $20^{\circ} C$ is