Question 148: Thermodynamics & KTG

Question

The magnitude of heat exchanged by a system for the given cyclic process ABCA (as shown in figure) is (in SI unit) :

Accepted Answer

Step 1: Find the Work Done ($$\mathrm{W}$$) in the Cycle
The work done in a cyclic process shown in a pressure-volume (P-V) graph is equal to the area enclosed by the cycle. For a circle, this area is $$\frac{1}{2} \pi R^2$$, where $$R$$ is the radius of the circle.
Step 2: Put in the Given Values
Radius $$R$$ on the graph is

$$ R = \frac{200}{2} 	imes 10^3 	ext{ (for Pressure, P)} \ R = \frac{200}{2} 	imes 10^{-6} 	ext{ (for Volume, V)} $$
Step 3: Calculate the Area (Work Done)
$$ \mathrm{W} = \frac{1}{2} 	imes \pi 	imes \left(\frac{200}{2} 	imes 10^3ight) 	imes \left(\frac{200}{2} 	imes 10^{-6}ight) $$
First, calculate $$\frac{200}{2} = 100$$, so:
$$ \mathrm{W} = \frac{1}{2} 	imes \pi 	imes 100 	imes 10^3 	imes 100 	imes 10^{-6} $$
Multiplying $$100 	imes 100 = 10,000$$, and $$10^3 	imes 10^{-6} = 10^{-3}$$, so:
$$ \mathrm{W} = \frac{1}{2} 	imes \pi 	imes 10,000 	imes 10^{-3} = \frac{1}{2} 	imes \pi 	imes 10 = 5\pi~\mathrm{J} $$
Step 4: Relate to Heat Exchanged
In a complete cycle, the change in internal energy is zero, so total heat exchanged is equal to the total work done.
So, the magnitude of heat exchanged is $$5\pi~\mathrm{J}$$.

Answer

zero

Answer

40$\pi$

Answer

5$\pi$

Answer

10$\pi$

Thermodynamics & KTG

The magnitude of heat exchanged by a system for the given cyclic process ABCA (as shown in figure) is (in SI unit) :

Choose the correct answer: