TS EAMCET · Physics · Thermodynamics

The efficiency of carnot engine is $η$ when its hot and cold reservoirs are maintained at temperature $T_{1}$ and $T_{2}$ , respectively. To increase the efficiency to $1.5 η$ , the increase in temperature $(Δ T)$ of the hot reservoir by keeping the cold one constant at $T_{2}$ is

A $\frac{T_{1} T_{2}}{(1 - η) (1 - 1.5 η)}$
B $\frac{0.5 T_{2} η}{(1 - 1.5 η) (1 - η)}$
C $\frac{T_{1}}{1 - η} - \frac{T_{2}}{1 - 1.5 η}$
D $\frac{(1 - η) (1 - 1.5 η)}{T_{1} T_{2}}$

Verified Solution

Answer & Solution

Correct Answer

(B) $\frac{0.5 T_{2} η}{(1 - 1.5 η) (1 - η)}$

Step-by-step Solution

Detailed explanation

The efficiency of Carnot engine is η=1-T2T1 ⇒T1T2=11-η The efficiency has to be increased to 1.5 η by maintaining T2 constant. ∴ 1.5η=1-T2T1+∆T⇒1.5η=1-T2T1+∆T…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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The efficiency of carnot engine is η when its hot and cold reservoirs are maintained at temperature T1 and T2, respectively. To increase the efficiency to 1.5 η, the increase in temperature ΔT of the hot reservoir by keeping the cold one constant at T2 is

Step-by-step Solution

The efficiency of carnot engine is $η$ when its hot and cold reservoirs are maintained at temperature $T_{1}$ and $T_{2}$ , respectively. To increase the efficiency to $1.5 η$ , the increase in temperature $(Δ T)$ of the hot reservoir by keeping the cold one constant at $T_{2}$ is