Question

The work done by 6 moles of helium gas when its temperature increases by \( 20^\circ \text{C} \) at constant pressure is (Universal gas constant = \( 8.31 \, \text{J mol}^{-1} \, \text{K}^{-1} \))

• A. \( 807.2 \, \text{J} \)
• B. \( 887.2 \, \text{J} \)
• C. \( 997.2 \, \text{J} \)
• D. \( 1007.2 \, \text{J} \)

Hint:

When calculating work done by an ideal gas at constant pressure, use the formula $ W = n R \Delta T $. Ensure all temperatures are in Kelvin.

Answer 1

The Correct Option is C

Step 1: Known Information. 
Number of moles of helium gas: \( n = 6 \)
Temperature increase: \( \Delta T = 20^\circ \text{C} = 20 \, \text{K} \)
Universal gas constant: \( R = 8.31 \, \text{J mol}^{-1} \, \text{K}^{-1} \) 
Step 2: Work Done at Constant Pressure. 
For an ideal gas at constant pressure, the work done is given by: $$ W = n R \Delta T $$ Step 3: Substitute Values. 
Substitute the known values: $$ W = 6 \cdot 8.31 \cdot 20 $$ Simplify: $$ W = 6 \cdot 166.2 = 997.2 \, \text{J} $$ Final Answer: \( \boxed{997.2 \, \text{J}} \)