1.7 mol of an ideal gas which starts at 1.6 atm and 50 o C does 2.0 kJ of work during an adiabatic expansion. What is the final volume of the gas?
P V^g = constant during an adiabatic expansion.
You need to know the value of the Cp/Cv specific heat ratio, g (usually called gamma) to compute the P dV integral (work done).
Just calling it an "ideal gas" is not enough. Gamma is 7/5 for diatomics and 5/3 for monatomic gases. Both can be ideal in terms of the gas law.
if you are paying money to take this course, you are beiung cheated.
For additional reading, I suggest
http://en.wikipedia.org/wiki/Adiabatic_process
To find the final volume of the gas, we can use the adiabatic expansion equation, which relates the initial and final properties of the gas. The equation is as follows:
P1 * V1^γ = P2 * V2^γ
Where:
P1 = initial pressure (in this case, 1.6 atm)
V1 = initial volume (which we don't know yet)
P2 = final pressure (which we also don't know yet)
V2 = final volume (what we're trying to find)
γ = heat capacity ratio (also known as the adiabatic index, which depends on the specific gas)
First, we need to find γ for this gas. For an ideal monoatomic gas like helium or argon, γ is approximately 5/3. Therefore, we'll assume γ = 5/3 in this case.
Now, we can plug in the given values and solve for V2:
P1 * V1^(5/3) = P2 * V2^(5/3)
Given that P1 = 1.6 atm, we need to express it in SI units (Pascal). 1 atm is equal to 101325 Pa, so:
P1 = 1.6 * 101325 = 162120 Pa
V1 is not given in the question, so we can't solve for V2 unless we know it. Please provide the value of V1 in order to proceed with the calculation.