A cylinder with a movable piston encloses 0.39 mole of ideal gas at 308K . How much heat is required to increase its volume isothermally by a factor of 3?
1100J
1400J
1600J
550J
To find the amount of heat required to increase the volume of the gas isothermally by a factor of 3, we can use the formula for the work done by an ideal gas during an isothermal process.
The formula for work done (W) by an ideal gas during an isothermal process is given by:
W = nRT * ln(Vf/Vi)
Where:
- n is the number of moles of the gas (in this case, given as 0.39 moles)
- R is the ideal gas constant (approximately 8.314 J/(mol·K))
- T is the temperature of the gas (in this case, given as 308 K)
- ln is the natural logarithm
- Vf is the final volume of the gas
- Vi is the initial volume of the gas
In this case, we need to increase the volume by a factor of 3, which means the final volume (Vf) will be 3 times the initial volume (Vi).
So, Vf = 3 * Vi
Substituting this value into the formula for work done:
W = nRT * ln(3)
Now we can calculate the value of W using the given values:
W = 0.39 mol * 8.314 J/(mol·K) * 308 K * ln(3)
Using a calculator, we find that ln(3) is approximately 1.0986.
W ≈ 0.39 mol * 8.314 J/(mol·K) * 308 K * 1.0986
W ≈ 1102.22 J
Therefore, the amount of heat required to increase the volume isothermally by a factor of 3 is approximately 1100 J.
So, the correct answer is 1100 J.