Solving 1.5 Moles Monatomic Ideal Gas at 314K - No Calc

[cdymdcool]

1. 1.5 moles of a monatomic ideal gas is enclosed at 314K. THe initial volume of the gas is 3m^3. The gas is comperssed isothermally to a final volume of 1m^3. How much heat is removed from the gas.



So deltaU=0, Q=-W, So we have to know the area under the P-V curve, but how can we get the solution without calculus?

 

[kuruman]

We can't. Algebra-based textbooks just provide the appropriate equation and justify it by saying that it can obtained by using calculus.

 

[kerimek]

One possible approach to solving this problem without using calculus would be to use the ideal gas law, PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature. We can rearrange this equation to solve for pressure (P = nRT/V), and then use this pressure value to calculate the work done on the gas during compression (W = PΔV). Since the process is isothermal, we know that the change in internal energy (ΔU) is equal to zero, and therefore the heat removed from the gas (Q) must be equal to the work done on the gas (Q = -W). By plugging in the known values for n, T, and the initial and final volumes, we can solve for the heat removed from the gas.