Thermodynamic problem, mastering physics

[Shayna]

Homework Statement
A 3000 cm³ container holds 0.10 mol of helium gas at 300C.
How much work must be done to compress the gas to 1000 cm³ at constant pressure?
How much work must be done to compress the gas to 1000 cm³ at constant temperature?


The attempt at a solution
W = integration p dv
For constant pressure,
because pressure is constant, therefore it matters not what integral it is on
W= p = nRT/v = 0.1*8.314*573.15/3 = 158.34


For constant temperature,
W= integration p dv over integral v=1L and v=3L
W= 317.6

apparently Mastering physics thinks this is neither here nor there, well, I am very

 

[alphysicist]

Hi Shayna,

Homework Statement
A 3000 cm³ container holds 0.10 mol of helium gas at 300C.
How much work must be done to compress the gas to 1000 cm³ at constant pressure?
How much work must be done to compress the gas to 1000 cm³ at constant temperature?


The attempt at a solution
W = integration p dv
For constant pressure,
because pressure is constant, therefore it matters not what integral it is on
W= p = nRT/v = 0.1*8.314*573.15/3 = 158.34

Looking at the first one, this does not look right to me. The work is not equal to the pressure (for one thing they don't have the same units).

You need to evaluate the integral:

$$W = - p \int\limits_{V_i}^{V_f} dV$$

In your work you have determined p, but the volume integral is not equal to 1, so there is more to the answer than just p. What do you get?

(Also, be careful with your units.)

 

[Shayna]

Okay, I start from scratch again and got the right answer
I've made multiple mistakes due to carelessness in term of unit.

Thanks so much