Question

If the volume of a balloon is expanded by 2L against a constant external pressure of 1.5 atm, how much heat energy would have to be added to maintain the same temperature?

a) 3 J
b) 1 J
c) 6 J
d) 4 J
e) 2 J

Answer 1

To maintain the same temperature when the volume of a balloon is expanded by 2L against a constant external pressure of 1.5 atm, 303.9 J of heat energy must be added. This is calculated using the formula W = -PΔV and converting atm to joules. none of the options are correct.

Step-by-step explanation:

The question asks how much heat energy would have to be added to maintain the same temperature if the volume of a balloon is expanded by 2L against a constant external pressure of 1.5 atm. To calculate the work done by the gas during isothermal expansion, we can use the formula W = -PΔV, where W is work, P is the external pressure, and ΔV is the change in volume. Here we know the external pressure (1.5 atm) and the change in volume (2L). We'll also need to convert the pressure from atm to joules using the conversion factor, 1 L·atm = 101.3 J.

W = -PΔV = (-1.5 atm)(2L) = -3 atm·L = -3 · 101.3 J/L·atm = -303.9 J

Since work done by the gas is negative, the heat added must be positive to maintain constant temperature (according to the first law of thermodynamics). Therefore, the amount of heat energy that must be added to the gas is 303.9 J. However, since the provided options only have integer numbers and are all significantly smaller than the calculated value, it may indicate an error in the question or the provided options.