Question

Four kilograms of carbon monoxide (CO) is contained in a rigid tank with a volume of 1 m^3. The tank is fitted with a paddle wheel that transfers energy to the CO at a constant rate of 14 W for 1 h. During the process, the specific internal energy of the carbon monoxide increases by 10 kJ/kg. If no overall changes in kinetic and potential energy occur,

determine:
a. the specific volume at the final state;
b. the energy transfer by work;
c. the energy transfer by heat transfer, and the direction of the heat transfer.

Answer 1

(a). The specific volume at the final state is 0.25 m³/kg.

(b). The energy transfer by work is 50.4 kJ.

(c). The energy transfer by heat is -10.4 kJ.

Negative sign shows the direction of heat

Step-by-step explanation:

Given that,

Weight of carbon monoxide = 4 kg

Volume of tank = 1 m³

Constant rate of 14W for 1 hour

The specific internal energy of the carbon monoxide increases by 10 kJ/kg.

(a). We need to calculate the specific volume at the final state

Using formula of specific volume

`V'=(V)/(m)`

Put the value into the formula

`V'=(1)/(4)`

`V'=0.25\ m^3/kg`

(b). We need to calculate the energy transfer by work

Using formula of work

`W=Pt`

Where, P = power

t = time

Put the value into the formula

`W=14*1*3600`

`W=50.4\ kJ`

(c). The energy transfer by heat transfer, and the direction of the heat transfer

We need to calculate the
`\Delta U`

Using formula of internal energy

`\Delta U=m\Delta u`

Put the value into the formula

`\Delta U=4*10`

`\Delta U=40\ kJ`

We need to calculate the energy transfer by heat

Using formula of energy transfer

`Q=\Delta U-W`

Put the value into the formula

`Q=40-50.4`

`Q=-10.4\ kJ`

Negative sign shows the direction of heat that is removed from CO.

Hence, (a). The specific volume at the final state is 0.25 m³/kg.

(b). The energy transfer by work is 50.4 kJ.

(c). The energy transfer by heat is -10.4 kJ.

Negative sign shows the direction of heat.