Find the work done W_{ABC} for the process A | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The work done in a $P-V$ diagram is given by the area under the curve,with a negative sign for expansion: $W = -\int P \, dV$.For the path $A \rig

Vedclass · Accepted Answer

$-37$

Vedclass · Answer

(B) The work done in a $P-V$ diagram is given by the area under the curve,with a negative sign for expansion: $W = -\int P \, dV$.For the path $A ightarrow B$,the process is a straight line. The area under the line $AB$ is a trapezoid with height $(V_B - V_A) = (5 - 1) = 4 \, L$ and parallel sides $P_A = 1 \, atm$ and $P_B = 5 \, atm$.Area $AB = \frac{1}{2} 	imes (P_A + P_B) 	imes (V_B - V_A) = \frac{1}{2} 	imes (1 + 5) 	imes 4 = \frac{1}{2} 	imes 6 	imes 4 = 12 \, L \cdot atm$.For the path $B ightarrow C$,the process is isobaric at $P = 5 \, atm$. The area under the line $BC$ is a rectangle with height $P = 5 \, atm$ and width $(V_C - V_B) = (10 - 5) = 5 \, L$.Area $BC = P 	imes (V_C - V_B) = 5 	imes 5 = 25 \, L \cdot atm$.The total area under the path $ABC$ is $12 + 25 = 37 \, L \cdot atm$.Since the process involves expansion ($V$ increases from $1 \, L$ to $10 \, L$),the work done by the system is negative: $W_{ABC} = -37 \, L \cdot atm$.

Find the work done $W_{ABC}$ for the process $A$ $\rightarrow B$ $\rightarrow C$ in $L \cdot atm$.

Similar Questions

The work done when the temperature of $1 \, \text{mol}$ of an ideal gas is increased by $2 \, ^\circ\text{C}$ is ......... $J$.

What is meant by standard state?

For one mole of an ideal gas,which of these statements must be true?
$(a)$ $U$ and $H$ each depend only on temperature.
$(b)$ Compressibility factor $Z$ is not equal to $1$.
$(c)$ $C_{P,m} - C_{V,m} = R$
$(d)$ $dU = C_V dT$ for any process.

Calculate work done if $1 \ mole$ of an ideal gas expands isothermally from $2 \ dm^3$ to $2.8 \ dm^3$ against constant external pressure $1 \ atm$. (in $J$)

Which of the following transformations is endothermic in nature?

Vedclass Test Series

Exam Paper Generator

Online Exam Module