One kilogram of ice at $0°$C is mixed with one kilogram of water at 80$°C$. The final temperature of the mixture is (Take: Specific heat of water = 4200 J $k{g}^{-1}{C}^{-1}$, Latent heat of ice = 336 kJ $k{g}^{-1}$)

1. $0°$C
2. $50°C$
3. $40°C$
4. $60°C$

Hot water cools from 60$°\mathrm{C}$ to 50$°\mathrm{C}$ in first 10 minutes and from 50$°\mathrm{C}$ to 42$°\mathrm{C}$ in next 10 minutes. The temperature of surrounding is :

1.  $5° \mathrm{C}$

2.  $10° \mathrm{C}$

3.  $15° \mathrm{C}$

4.  $20°\mathrm{C}$

Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is at ${100}^{°}$ C, while the other one is at $0^{° }$C. If the two bodies are brought into contact, then assuming no heat loss, the final common temperature is -

1. ${50}^{°} C$

2. more than ${50}^{°}$C

3. less than ${50}^{°}$C but greater than $0^{°}$C

4.  $0 {}_{0}C$

Steam at 100°C is passed into 20 g of water at 10°C. When water acquires a temperature of 80°C, the mass of water present will be (Take specific heat of water=1 cal g^-1 °C^-1 and latent heat of steam = 540 cal g^-1)

(a) 24 g                       

(b) 31.5g

(c) 42.5 g                   

(d) 22.5 g

A certain quantity of water cools from \(70^{\circ}\mathrm{C}\) to \(60^{\circ}\mathrm{C}\) in the first 5 minutes and to \(54^{\circ}\mathrm{C}\) in the next 5 minutes. 
The temperature of the surroundings will be: 

Liquid oxygen at 50K is heated to 300K at constant pressure of 1 atm. The rate of heating is constant.Which one of the following graphs represents the variation of temperature with time?

A black body at $227°C$ radiates heat at the rate of 7 cal $c{m}^{-2}{s}^{-1}.$ At a temperature of $727°C,$ the rate of heat radiated in the same units will be 

1. 60                                     

2. 50

3. 112                                   

4. 80

On a new scale of temperature (which is linear) and called the W scale, the freezing and boiling points of water are $39°W$ and $239°W$ respectively. What will be the temperature on the new scale, corresponding to a temperature of $39°C$ on the Celsius scale?

1. $78°W$                                   

2. $117°W$

3. $200°W$                                 

4. $139°W$

A metal bar of length \(L\) and area of cross-section \(A\) is clamped between two rigid supports. For the material of the rod, it's Young’s modulus is \(Y\) and the coefficient of linear expansion is \(\alpha.\) If the temperature of the rod is increased by \(\Delta t^{\circ} \text{C},\) the force exerted by the rod on the supports will be:
1. \(YAL\Delta t\)
2. \(YA\alpha\Delta t\)
3. \(\frac{YL\alpha\Delta t}{A}\)
4. \(Y\alpha AL\Delta t\)

The coefficient of linear expansion of brass and steel are ${\alpha }_1$ and ${\alpha }_2$. If we take a brass rod of length $l_1$ and steel rod of length $l_2$ at 0°C, their difference in length $\left(l_2-l_1\right)$ will remain the same at a temperature if

1. ${\alpha }_1{l}_2={\alpha }_2{l}_1$                                   
2. ${\alpha }_1{l}_2^2={\alpha }_2{l}_1^2$
3. ${\alpha }_1^2{l}_1={\alpha }_2^2{l}_2$                                   
4. ${\alpha }_1{l}_1={\alpha }_2{l}_2$