The internal energy of the air, in a room of volume V, at temperature T and with outside pressure p increasing linearly with time, varies as 

Options

A. increases linearly
B. increases exponentially
C. decreases linearly
D. remains constant

Answer

A

Explanation

Using first law of thermodynamics,
`dU-dQ-dW`
Here, `dW=pdV=0(V="constant")`
`:.` Change in internal energy, dU = dQ
`dU prop dT" "(dQ=C_(v)dT)`
Using, `" "pV=RT`
`dT=(V)/( R )dp`
`implies" "dT prop dp`
`implies" "dU prop dp`
Hence, internal energy will increase with increment in pressure.