Question 869: Thermodynamics & KTG

Question

Which of the following statements is true?
($$\Delta \mathrm{U}=$$ increase in internal energy, $$\mathrm{dW}=$$ work done by the system)

Accepted Answer

In thermodynamics, understanding the relationships between internal energy, work, and heat for different types of processes is crucial. Let's analyze the options given:
First, letÃ¢ÂÂs recall the first law of thermodynamics, which states:
$$\Delta \mathrm{U} = \mathrm{Q} - \mathrm{W}$$
Here:
$$\Delta \mathrm{U}$$ = Change in internal energy
$$\mathrm{Q}$$ = Heat added to the system
$$\mathrm{W}$$ = Work done by the system
Now, letÃ¢ÂÂs consider each type of process:
Adiabatic Process:
In an adiabatic process, no heat is exchanged with the surroundings, so $$\mathrm{Q} = 0$$. This simplifies the first law of thermodynamics to:
$$\Delta \mathrm{U} = -\mathrm{W}$$
This means that the change in internal energy is equal to the negative of the work done by the system.
Therefore, the correct statement in the context of an adiabatic process is:
Option B:
In an adiabatic process $$\Delta \mathrm{U}=-\mathrm{dW}$$
Isothermal Process:
In an isothermal process, the temperature remains constant, which implies that there is no change in internal energy for an ideal gas. So:
$$\Delta \mathrm{U} = 0$$
According to the first law of thermodynamics:
$$0 = \mathrm{Q} - \mathrm{W}$$
This simplifies to:
$$\mathrm{Q} = \mathrm{W}$$
Therefore, there is no direct relationship between $$\Delta \mathrm{U}$$ and $$\mathrm{W}$$ in an isothermal process other than that $$\Delta \mathrm{U} = 0$$.
So, options C and D are not correct regarding isothermal processes.
Conclusion:
The correct answer is:
Option B: In an adiabatic process $$\Delta \mathrm{U}=-\mathrm{dW}$$

Answer

In an adiabatic process $$\Delta \mathrm{U}=\mathrm{dW}$$

Answer

In an adiabatic process $$\Delta \mathrm{U}=-\mathrm{dW}$$

Answer

In an isothermal process $$\Delta \mathrm{U}=-\mathrm{dW}$$.

Answer

In an isothermal process $$\Delta \mathrm{U}=\mathrm{dW}$$

Thermodynamics & KTG

Which of the following statements is true? ($\Delta \mathrm{U}= increase in internal energy, \mathrm{dW}=$ work done by the system)

Choose the correct answer: