Question

0.0884 moles of a diatomic gas

are in a piston. When the piston
is compressed, the temperature
drops by 18.8 K, and 83.7 J of
heat flow out. Find W.
(Be careful with + and - signs.
+W = expansion, +Q = added,
+AU = temp goes up)
(Unit = J)

Answer 1

-49.2

Step-by-step explanation:

Trust me bro

Answer 2

W = - 118.24 J (negative sign shows that work is done on piston)

Step-by-step explanation:

First, we find the change in internal energy of the diatomic gas by using the following formula:

`\Delta\ U = nC_(v)\Delta\ T`

where,

ΔU = Change in internal energy of gas = ?

n = no. of moles of gas = 0.0884 mole

Cv = Molar Specific Heat at constant volume = 5R/2 (for diatomic gases)

Cv = 5(8.314 J/mol.K)/2 = 20.785 J/mol.K

ΔT = Rise in Temperature = 18.8 K

Therefore,

`\Delta\ U = (0.0884\ moles)(20.785\ J/mol.K)(18.8\ K)\\\Delta\ U = 34.54\ J`

Now, we can apply First Law of Thermodynamics as follows:

`\Delta\ Q = \Delta\ U + W`

where,

ΔQ = Heat flow = - 83.7 J (negative sign due to outflow)

W = Work done = ?

Therefore,

`-83.7\ J = 34.54\ J + W\\W = -83.7\ J - 34.54\ J\\`

W = - 118.24 J (negative sign shows that work is done on piston)