JEE Main - 25 January 2023 Shift 1

If $K_1$ and $K_2$ are the thermal conductivities $L_1$ and $L_2$ are the lengths and $A_1$ and $A_2$ are the cross sectional areas of steel and copper rods respectively such that $\frac{K_2}{K_1}=9,\frac{A_1}{A_2}=2,\frac{L_1}{L_2}=2$. Then, for the arrangement as shown in the figure. The value of temperature $T$ of the steel - copper junction in the steady state will be

Two metallic wires of identical dimensions are connected is series. If ${\sigma }_1$ and ${\sigma }_2$ are the conductivities of the these wires respectively, the effective conductivity of the combination is :

A hole is drilled in a metal sheet. At $27 °\mathrm{C}$, the diameter of hole is $5 \mathrm{cm}$. When the sheet is heated to $177 °\mathrm{C}$, the change in the diameter of hole is $d\times {10}^{-3} \mathrm{cm}$ . The value of $d$ will be _____, if coefficient of linear expansion of the metal is $1.6\times {10}^{-5}/{}^{\circ }\mathrm{C}$ 

The graph between two temperature scales $P$ and $Q$ is shown in the figure. Between upper fixed point and lower fixed point there are $150$ equal divisions of scale $P$ and $100$ divisions on scale $Q$. The relationship for conversion between the two scales is given by :

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A body cools from $60°\mathrm{C}$ to $40°\mathrm{C}$ in $6$ minutes. If, temperature of surroundings is $10°\mathrm{C}$. Then, after the next $6$ minutes, its temperature will be ______ $°\mathrm{C}$.

Heat energy of $184 \mathrm{kJ}$ is given to ice of mass $600 \mathrm{g}$ at $-12 °\mathrm{C}$, Specific heat of ice is $2222.3 \mathrm{J} {\mathrm{kg}}^{–1} °{\mathrm{C}}^{–1}$, and the latent heat of ice is $336 \mathrm{kJ} {\mathrm{kg}}^{–1}$. Consider the statements below.

(A) Final temperature of the system will be $0 °\mathrm{C}$

(B) Final temperature of the system will be greater than $0 °\mathrm{C}$

(C) The final system will have a mixture of ice and water in the ratio of  $5 : 1$

(D) The final system will have a mixture of ice and water in the ratio of  $1 : 5$

(E) The final system will have water only

Choose the correct answer from the options given below :

The pressure $\left(P\right)$ and temperature $\left(T\right)$ relationship of an ideal gas obeys the equation $P{T}^2=$ constant. The volume expansion coefficient of the gas will be :

A faulty thermometer reads $5°\mathrm{C}$ in melting ice and $95°\mathrm{C}$ in steam. The correct temperature on absolute scale will be ______ $\mathrm{K}$ when the faulty thermometer reads $41°\mathrm{C}$.