Question

A cylinder of fixed capacity 44.81 contains hydrogen gas at STP. What is the amount of heat needed to raise the temperature of the gas in the cylinder by 20° C? $ (R = 8.31 \, \text{J mol}^{-1} \, \text{K}^{-1}) $

• A. 541 J
• B. 374 J
• C. 831 J
• D. 743 J

Hint:

To find the heat required to raise the temperature of a gas, use the formula \( Q = n C \Delta T \), where \( n \) is the number of moles, \( C \) is the molar heat capacity, and \( \Delta T \) is the change in temperature.

Answer 1

The Correct Option is C

The amount of heat needed to raise the temperature of a gas is given by the formula: \[ Q = n C \Delta T \] Where: 
- \( n \) is the number of moles of the gas, 
- \( C \) is the molar heat capacity at constant volume, 
- \( \Delta T \) is the change in temperature. 
Given: - The gas is hydrogen, so \( C = 8.31 \, \text{J mol}^{-1} \, \text{K}^{-1} \), - The cylinder's capacity is \( 44.81 \, \text{L} \), and at STP, 1 mole of gas occupies 22.4 L, so: \[ n = \frac{44.81}{22.4} \approx 2 \, \text{mol} \] - The temperature change is \( \Delta T = 20 \, \text{C} \). Now, substitute the values: \[ Q = 2 \, \text{mol} \times 8.31 \, \text{J mol}^{-1} \, \text{K}^{-1} \times 20 \, \text{K} \] \[ Q = 831 \, \text{J} \] 
Thus, the amount of heat needed is 831 J.