Thermodynamics

ΔU ≈ 2.09 × 10⁶ J

Step 1: Heat absorbed Q = mL = 1 × 2.26 × 10⁶ = 2.26 × 10⁶ J. Step 2: Work done by the system W = P × ΔV = P(Vᵥ - Vₗ) = 1.01 × 10⁵ × (1.671 - 0.001) = 1.01 × 10⁵ × 1.670 = 1.6867 × 10⁵ ≈ 1.69 × 10⁵ J. Step 3: By First Law: ΔU = Q - W = 2.26 × 10⁶ - 1.69 × 10⁵ = 2.26 × 10⁶ - 0.169 × 10⁶ ≈ 2.091 × 10⁶ J. Step 4: So ΔU ≈ 2.09 × 10⁶ J. Step 5: The heat supplied is used partly in increasing internal energy (breaking molecular bonds) and partly in doing external work (against atmospheric pressure). Option B ignores the work done. Option C is just the work done. Option D is wrong - temperature is con

Change in internal energy (ΔU)

Step 1: Internal energy U is a state function - it depends only on the state of the system, not on the path taken to reach that state. Step 2: Since both paths start from the same initial state i and end at the same final state f, ΔU = U_f - U_i is the same for both paths. Step 3: Work done W depends on the path (W = ∫PdV). The area under Path iaf is larger than under Path ibf (as shown by the P-V diagram analysis in the textbook). Step 4: Since Q = ΔU + W and ΔU is same but W is different, Q must also be different for the two paths. Step 5: This is the fundamental distinction between state fu

400 J

Step 1: In an isochoric process, the volume remains constant (ΔV = 0). Step 2: Work done by the gas: W = P × ΔV = P × 0 = 0 J. Step 3: Apply the First Law: ΔU = Q - W = 400 - 0 = 400 J. Step 4: All the heat supplied goes entirely into increasing the internal energy of the gas. Step 5: The pressure change data (from 2 × 10⁵ to 5 × 10⁵ Pa) is extra information - it does not affect the calculation because in an isochoric process, work done is always zero regardless of pressure change. This is a common trick in hard-level questions - don't be misled by extra data. Explosions in closed chambers are

Since T_A = T_C and T_B = T_C, it follows that T_A = T_B, meaning no net heat transfer occurs between A and B.

Step 1: Thermal equilibrium between two bodies means their temperatures are equal and there is no net heat flow between them. Step 2: If A is in thermal equilibrium with C, then T_A = T_C. Step 3: If B is in thermal equilibrium with C, then T_B = T_C. Step 4: From Step 2 and 3: T_A = T_C = T_B, so T_A = T_B. Equal temperatures mean no net heat transfer between A and B, so they are in thermal equilibrium. Step 5: The Zeroth Law does NOT require same mass, specific heat, internal energy, or material - it is purely about temperature equality. This law is the basis for defining temperature as a me