Find out the correct match. a.First law of thermodynamics b.isothermal change c.state function d.adiabatic change i.`DeltaU=W` ii.q=-W iii.q+W. iv.`DeltaU=q+W`

Options

A. a(iv),b(ii),c(iii),d(iv)
B. a(ii),b(iii),c(iv),d(i)
C. a(iv),b(i),c(ii),d(iii)
D. a(I),b(iv),c(ii),d(iii)

Answer

To solve the question, we need to match the terms with their correct definitions or equations. Let's break it down step by step:

### Step 1: Understand the First Law of Thermodynamics
The first law of thermodynamics states that the change in internal energy (ΔU) of a system is equal to the heat added to the system (Q) plus the work done on the system (W). This can be expressed as:
\[ \Delta U = Q + W \]

### Step 2: Match the First Law of Thermodynamics
From the equation we derived in Step 1, we can see that:
- **a. First law of thermodynamics** matches with **iv. ΔU = Q + W**.

### Step 3: Analyze Isothermal Change
In an isothermal process, the temperature remains constant (ΔT = 0). For an ideal gas, this means that the change in internal energy (ΔU) is zero:
\[ \Delta U = 0 \]
Thus, from the first law:
\[ 0 = Q + W \]
This implies:
\[ Q = -W \]
So, **b. Isothermal change** matches with **ii. Q = -W**.

### Step 4: Identify State Function
A state function is a property that depends only on the state of the system, not on how it got there. The change in internal energy (ΔU) is a state function. Therefore, we can say:
- **c. State function** matches with **iii. ΔU is a state function**.

### Step 5: Analyze Adiabatic Change
In an adiabatic process, there is no heat exchange with the surroundings (Q = 0). Applying the first law:
\[ \Delta U = Q + W \]
Since Q = 0, we have:
\[ \Delta U = W \]
Thus, **d. Adiabatic change** matches with **i. ΔU = W**.

### Final Matching
Now we can summarize the matches:
- a. First law of thermodynamics → iv. ΔU = Q + W
- b. Isothermal change → ii. Q = -W
- c. State function → iii. ΔU is a state function
- d. Adiabatic change → i. ΔU = W

### Summary of Matches
- a → iv
- b → ii
- c → iii
- d → i