1.
12 identical rods made of same material are arranged in the form of a cube. The temperature of $$P$$ and $$R$$ are maintained at $${90^ \circ }C$$ and $${30^ \circ }C$$ respectively. Then the temperature of point $$V,$$ when steady state is reached is
2.
A mass of $$50g$$ of water in a closed vessel, with surroundings at a constant temperature takes $$2$$ minutes to cool from $${30^ \circ }C$$ to $${25^ \circ }C.$$ A mass of $$100g$$ of another liquid in an identical vessel with identical surroundings takes the same time to cool from $${30^ \circ }C$$ to $${25^ \circ }C.$$ The specific heat of the liquid is: (The water equivalent of the vessel is $$30g.$$ )
3.
A hammer of mass $$1\,kg$$ having speed of $$50\,m/s,$$ hit a iron nail of mass $$200\,gm.$$ If specific heat of iron is $$0.105\,cal/g{m^ \circ }C$$ and half the energy is converted into heat. the raise in temperature of nail is
4.
Liquid oxygen at $$50\,K$$ is heated to $$300\,K$$ 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?
Graph (A) shows the variation of temperature with time. At first temperature will increase then there will be state change from liquid to gas.
5.
If liquefied oxygen at 1 atmospheric pressure is heated from $$50\,k$$ to $$300\,k$$ by supplying heat at constant rate. The graph of temperature vs time will be
$$\eqalign{
& Q = mc\,\Delta T \cr
& \Rightarrow \,\,Q = mc\left( {T - {t_0}} \right)\,\,\,.....\left( {\text{i}} \right) \cr} $$
∴ From $$50\,K$$ to boiling temperature, $$T$$ increases linearly.
During boiling, equation is
$$Q = mL$$
Temperature remains constant till boiling is complete After that, again eqn. (i) is followed and temperature increases linearly.
6.
A piece of ice falls from a height $$h$$ so that it melts completely. Only one-quarter of the heat produced is absorbed by the ice and all energy of ice gets converted into heat during its fall. The value of $$h$$ is [Latent heat of ice is $$3.4 \times {10^5}J/kg$$ and $$g = 10\,N/kg$$ ]
According to question as conservation of energy, energy gained by the ice during its fall from height $$h$$ is given by $$E = mgh$$
As given, only one quarter of its energy is absorbed by the ice.
$$\eqalign{
& {\text{So,}}\,\frac{{mgh}}{4} = m{L_f} \Rightarrow h = \frac{{m{L_f} \times 4}}{{mg}} \cr
& = \frac{{{L_f} \times 4}}{g} = \frac{{3.4 \times {{10}^5} \times 4}}{{10}} \cr
& = 13.6 \times {10^4} = 136000\,m = 136\,km \cr} $$
7.
A block of ice at $$ - {10^ \circ }C$$ is slowly heated and converted to steam at $${100^ \circ }C.$$ Which of the following curves represents the phenomenon qualitatively
Initially, on heating temperature rises from $$ - {100^ \circ }C$$ to $$ - {0^ \circ }C.$$ Then ice melts and temperature does not rise. After the whole ice has melted, temperature begins to rise until it reaches $${100^ \circ }C.$$ then it becomes constant, as at the boiling point will not rise.
8.
Assuming no heat losses, the heat released by the condensation of $$xg$$ of steam at $${100^ \circ }C$$ can be used to convert $$yg$$ of ice at $${0^ \circ }C$$ into water at $${100^ \circ }C,$$ the ratio $$x:y$$ is:
The heat lost in condensation $$ = x \times 540\,cal.$$
$$\eqalign{
& \therefore x \times 540 = y \times 80 + y \times 1 \times \left( {100 - 0} \right) \cr
& {\text{or}}\,\,\frac{x}{y} = \frac{1}{3}. \cr} $$
9.
The room heater can maintain only $${16^ \circ }C$$ in the room when the temperature outside is $${-20^ \circ }C.$$ It is not warm and comfortable, that is why the electric stove with power of $$1kW$$ is also plugged in. Together these two devices maintain the room temperature of $${22^ \circ }C.$$ Determine the thermal power of the heater.
Rate of heat loss with only room heater
$${P_h} = \frac{{\Delta Q}}{{\Delta t}} = C\left( {16 + 20} \right),C = {\text{constant}}$$
while for both heater and stove it is
$$\eqalign{
& {P_h} + {P_s} = {\left( {\frac{{\Delta Q}}{{\Delta t}}} \right)^\prime } = C\left( {22 + 20} \right) \cr
& \frac{{{P_h}}}{{{P_h} + {P_s}}} = \frac{{36}}{{42}} \Rightarrow 7{P_h} = 6{P_h} + 6{P_s} \cr
& \Rightarrow {P_h} = 6{P_s} = 6\,kW \cr} $$
10.
In an energy recycling process, $$100\,g$$ of steam at $${100^ \circ }C$$ becomes water at $${100^ \circ }C$$ which converts $$yg$$ of ice at $${0^ \circ }C$$ into water at $${100^ \circ }C.$$ The numeric value of $$y$$ is