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A piston filled with 0.04 mol of an idea...

A piston filled with `0.04` mol of an ideal gas expands reversibly from `50.0 mL` to `375 mL` at a constant temperature of `37.0^(@)C`. As it does so, it absorbs `208 J` of heat. The value of `q` and `w` for the process will be:
`(R=8.314J//molK)(ln 7.5=2.01)`

A

`q = - 208 J , w = + 208J`

B

`q = +208J,w = + 208 J`

C

`q = + 208 J, w = -208 J`

D

` q = -208 J , w = - 208 J`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to find the values of \( q \) (heat absorbed) and \( w \) (work done) for the given process. ### Step 1: Identify the heat absorbed The problem states that the gas absorbs \( 208 \, J \) of heat. Since the process is endothermic (heat is absorbed), we can denote this as: \[ q = +208 \, J \] ### Step 2: Relate heat and work in a reversible process For a reversible process, there is a relationship between heat absorbed (\( q \)) and work done (\( w \)): \[ q = -w \] This means that the work done by the system is equal in magnitude but opposite in sign to the heat absorbed. ### Step 3: Calculate work done From the relationship \( q = -w \), we can rearrange it to find \( w \): \[ w = -q \] Substituting the value of \( q \): \[ w = -208 \, J \] ### Summary of Results Thus, the values for the process are: - \( q = +208 \, J \) - \( w = -208 \, J \) ### Final Answer The values of \( q \) and \( w \) for the process are: - \( q = 208 \, J \) - \( w = -208 \, J \)
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