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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 :

Answer:

(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

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

[tex]V'=\dfrac{V}{m}[/tex]

Put the value into the formula

[tex]V'=\dfrac{1}{4}[/tex]

[tex]V'=0.25\ m^3/kg[/tex]

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

Using formula of work

[tex]W=Pt[/tex]

Where, P = power

t = time

Put the value into the formula

[tex]W=14\times1\times3600[/tex]

[tex]W=50.4\ kJ[/tex]

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

We need to calculate the [tex]\Delta U[/tex]

Using formula of internal energy

[tex]\Delta U=m\Delta u[/tex]

Put the value into the formula

[tex]\Delta U=4\times10[/tex]

[tex]\Delta U=40\ kJ[/tex]

We need to calculate the energy transfer by heat

Using formula of energy transfer

[tex]Q=\Delta U-W[/tex]

Put the value into the formula

[tex]Q=40-50.4[/tex]

[tex]Q=-10.4\ kJ[/tex]

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.

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