Thermodynamics first law closed system

[jordan2delta]

1) A rigid walled tank 5m3 contains helium at 10 bar. The cylinder is heated from 10 °C to 50 ° C. What is the work done during the heating cycle.

 

[jordan2delta]

how can determinate the work done during the heating cycle?
W=integral of pDV

which expression can I use to get the work done during the heating cycle?any advice?


1) A rigid walled tank 5m3 contains helium at 10 bar. The cylinder is heated from 10 °C to 50 ° C. What is the work done during the heating cycle.

 

[jordan2delta]

2) An expanding gas storage vessel contains 5 m3 of methane at 1.1 bar. On a hot day the gas is heated from 20 °C to 35 °C. What work is done by the gas on its surroundings

expression to calculate the work by the gas on the surroundings?
knowing that V=5m^3
p=1.1bar
t1=20 degree Celsius
t2= 35 degree Celsius
t2=

 

[jordan2delta]

3)One mole of CO2 is charged to a piston at 10 bar pressure 293K. The piston is allowed to expand to 4 times its volume isothermally. What work is done on the surroundings? The gas behaves ideally

A more complicated example using a polyatomic gas
Part1
– CO2 is charged at 2 bar to a piston at 298 K volume 0.5 m3. It is known to vary as polytonic gas PV2=C. The gas is allowed to expand isothermally to twice its volume what work is done by the system

Part 2
– A Spring force (5 kN/m extension) is added to retain the piston what work is done this time if the expansion is the same and how much work is done against the spring the piston area is 0.1 m2

please help me! I really need formulas to determinate work done by the system, and the work against the spring

 

[rezeew]

The first law of thermodynamics states that energy cannot be created or destroyed, only transferred or converted from one form to another. In the case of a closed system, such as the rigid walled tank described, the total energy within the system remains constant.

In this scenario, the work done during the heating cycle can be calculated using the equation W = PΔV, where W is work, P is pressure, and ΔV is the change in volume. Since the tank is rigid, the volume remains constant at 5m3. Therefore, the work done can be calculated by multiplying the change in pressure by the constant volume.

In this case, the change in pressure is 10 bar (from 10 bar to 20 bar) and the volume is 5m3. This gives us a work done of 50 bar*m3.

It is important to note that this calculation assumes that the heating process is carried out slowly and in a controlled manner, allowing the system to reach thermal equilibrium. If the heating process is not carried out in this manner, the work done may differ. Additionally, this calculation only takes into account the work done by the gas within the tank and does not consider any external work done on the system.