MCQ
A Camot cycle consists of
- ATwo stages
- ✓Four stages
- CSix stages
- DEight stages
This cycle is one of the foundations of the second law of thermodynamics, and Carnot is often considered the father of thermodynamics. He was one of the pioneers who first determined an idealistic way of converting heat energy into work done. Carnot cycle is one of the most efficient heat engines.
Carnot cycle consists of the following four processes:
$I.$ The gas goes through an isothermal expansion at a high temperature. In this process the gas takes $q_{\text {in }}$ amount of heat from the surrounding and does $w_1$ amount of work on the surrounding.
$II.$ The gas then undergoes a reversible adiabatic expansion. Hence, the temperature of the gas comes down to a lower temperature $T_{\text {low }}$.
$III.$ Then the gas is compressed isothermally at $T_{\text {low }}$ temperature. In this process, the gas loses $q_{\text {out }}$ amount of heat, and surroundings do work on the gas.
$IV.$ Now the gas goes through a reversible adiabatic compression which makes the temperature rise up to $T_{\text {high }}$.
The following diagram shows the $P-V$ diagram of the Carnot's cycle.
Hence, Carnot's cycle consists of two isothermal and two adiabatic processes.
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$\pi\text{s}.$
$\frac{\pi}{2}\ \text{s}.$
$2\pi\ \text{s}.$
$\frac{\pi}{\text{t}}\ \text{s}.$
A musical instrument is made using four different metal strings, $1,2,3$ and $4$ with mass per unit length $\mu, 2 \mu, 3 \mu$ and $4 \mu$ respectively. The instrument is played by vibrating the strings by varying the free length in between the range $L _0$ and $2 L _0$. It is found that in string-$1$ $(\mu)$ at free length $L _0$ and tension $T _0$ the fundamental mode frequency is $f _0$.
$List-I$ gives the above four strings while $list-II$ lists the magnitude of some quantity.
| $List-I$ | $List-II$ |
| $(I)$ String-1( $\mu$ ) | $(P) 1$ |
| $(II)$ String-2 $(2 \mu)$ | $(Q)$ $1 / 2$ |
| $(III)$ String-3 $(3 \mu)$ | $(R)$ $1 / \sqrt{2}$ |
| $(IV)$ String-4 $(4 \mu)$ | $(S)$ $1 / \sqrt{3}$ |
| $(T)$ $3 / 16$ | |
| $(U)$ $1 / 16$ |
($1$) If the tension in each string is $T _0$, the correct match for the highest fundamental frequency in $f _0$ units will be,
$(1)$ $I \rightarrow P , II \rightarrow R , III \rightarrow S , IV \rightarrow Q$
$(2)$ $I \rightarrow P , II \rightarrow Q , III \rightarrow T , IV \rightarrow S$
$(3)$ $I \rightarrow Q , II \rightarrow S , III \rightarrow R , IV \rightarrow P$
$(4)$ I $\rightarrow Q , II \rightarrow P , III \rightarrow R$, IV $\rightarrow T$
($2$) The length of the string $1,2,3$ and 4 are kept fixed at $L _0, \frac{3 L _0}{2}, \frac{5 L _0}{4}$ and $\frac{7 L _0}{4}$, respectively. Strings $1,2,3$ and 4 are vibrated at their $1^{\text {tt }}, 3^{\text {rd }}, 5^{\text {m }}$ and $14^{\star}$ harmonics, respectively such that all the strings have same frequency. The correct match for the tension in the four strings in the units of $T _0$ will be.
$(1)$ $I \rightarrow P , II \rightarrow Q , III \rightarrow T , IV \rightarrow U$
$(2)$ $I \rightarrow T , II \rightarrow Q , III \rightarrow R$, IV $\rightarrow U$
$(3)$ $I \rightarrow P , II \rightarrow Q , III \rightarrow R , IV \rightarrow T$
$(4)$ I $\rightarrow P , II \rightarrow R , III \rightarrow T , IV \rightarrow U$
If $v_1\,\,sin\,\,\theta _1 = v_2\,\,sin\,\,\theta _2$, then choose the incorrect statement