JEE Mains · Physics · STD 11 - 10.1, thermonetry,thermal expansion and calorimetry
- JEE Mains 2020
- Hard
- Numerical
Three containers \(\mathrm{C}_{1}, \mathrm{C}_{2}\) and \(\mathrm{C}_{3}\) have water at different temperatures. The table below shows the final temperature \(T\) when different amounts of water (given in litres) are taken from each containers and mixed (assume no loss of heat during the process) \(\begin{array}{|c|c|c|c|}\hline \mathrm{C_{1 }} & {\mathrm{C}_{2}} & {\mathrm{C}_{3}} & {\mathrm{T}} \\ \hline {1 l} & {2 l} & {-} & {60^{\circ} \mathrm{C}} \\ \hline {-} & {1 l} & {2 l} & {30^{\circ} \mathrm{C}} \\ \hline {2 l} & {-} & {1 l} & {60^{\circ} \mathrm{C}} \\ \hline {1 l} & {1 l} & {1 l} & {\theta} \\ \hline\end{array}\) The value of \(\theta\) (in \(^{\circ} \mathrm{C}\) to the nearest integer) is
Pick an option to check your answer.
Answer & Solution
Correct Answer
(D) \(50\)
Step-by-step Solution
Detailed explanation
According to table and applying law of calorimetry
\(1 \mathrm{T}_{1}+2 \mathrm{T}_{2}=(1+2) 60^{\circ}\)
\(=180\)
\(1 \mathrm{T}_{2}+2 \mathrm{T}_{3}=(1+2) 30^{\circ}\)
\(=90\)
\(2 \mathrm{T}_{1}+1 \mathrm{T}_{3}=(1+2) 60\)
\(=180\)
\(3\left(\mathrm{T}_{1}+\mathrm{T}_{2}+\mathrm{T}_{3}\right)=450\)
\(\mathrm{T}_{1}+\mathrm{T}_{2}+\mathrm{T}_{3}=150^{\circ}\)
Hence,
\(\mathrm{T}_{1}+\mathrm{T}_{2}+\mathrm{T}_{3}=(1+1+1) \theta\)
\(150=3 \theta\)
\(\theta=50^{\circ} \mathrm{C}\)
More questions from Physics
- A copper wire of length \(3\text{ m}\) is stretched by \(3\text{ mm}\) by applying an external force. The volume of the wire is \(600 \times 10^{-6}\text{ m}^3\). The elastic potential energy stored in the wire in stretched condition would be _______ J.
(Given Young modulus of copper \(= 1.1 \times 10^{11}\text{ N/m}^2\))JEE Mains 2026 Medium - Moment of inertia of a cylinder of mass \(M,\) length \(L\) and radius \(R\) about an axis passing through its centre and perpendicular to the axis of the cylinder is \(I = M \left(\frac{ R ^{2}}{4}+\frac{ L ^{2}}{12}\right) .\) If such a cylinder is to be made for a given mass of material, the ratio \(\frac LR\) for it to have minimum possible \(I\) isJEE Mains 2020 Hard
- Identify the logic operation carried out by the given circuit :-
JEE Mains 2021 Medium - If it takes \(5\,minutes\) to fill a \(15\,litre\) bucket from a water tap of diameter \(\frac{2}{{\sqrt \pi }}cm\) then the Reynolds number for the flow is (density of water \(= 10^3\,kg/m^3\) ) and viscosity of water \(= 10^{-3}\,Pa.s\) ) close toJEE Mains 2015 Hard
- A solid sphere of mass \(1\,kg\) rolls without slipping on a plane surface. Its kinetic energy is \(7 \times 10^{-3}\,J\). The speed of the centre of mass of the sphere is \(.........cm s ^{-1}\).JEE Mains 2023 Medium
- \(B _{ X }\) and \(B _{ Y }\) are the magnetic field at the centre of two coils of two coils \(X\) and \(Y\) respectively, each carrying equal current. If coil \(X\) has \(200\) turns and \(20 cm\) radius and coil \(Y\) has \(400\) turns and \(20 cm\) radius, the ratio of \(B _{ X }\) and \(B _{ Y }\) isJEE Mains 2022 Medium
More PYQs from JEE Mains
- The fractional compression \(\left(\frac{\Delta \mathrm{V}}{\mathrm{V}}\right)\) of water at the depth of 2.5 km below the sea level is ______ \(\%\). Given, the Bulk modulus of water \(=2 \times 10^9 \mathrm{~N} \mathrm{~m}^{-2}\), density of water \(=10^3\) \(\mathrm{kg} \mathrm{m}^{-3}\), acceleration due to gravity \(=\mathrm{g}=10 \mathrm{~m} \mathrm{~s}^{-2}\).JEE Mains 2025 Medium
- Find the mutual inductance in the arrangement, when a small circular loop of wire of radius ' \(R\) ' is placed inside a large square loop of wire of side \(L\) \(( L \gg R )\). The loops are coplanar and their centres coincide :
JEE Mains 2023 Medium - A student determined Young's Modulus of elasticity using the formula \(Y=\frac{M g L^{3}}{4 b d^{3} \delta} .\) The value of \(g\) is taken to be \(9.8 \,{m} / {s}^{2}\), without any significant error, his observation are as following.
Then the fractional error in the measurement of \({Y}\) isPhysical Quantity Least count of the Equipment used for measurement Observed value Mass \(({M})\) \(1\; {g}\) \(2\; {kg}\) Length of bar \((L)\) \(1\; {mm}\) \(1 \;{m}\) Breadth of bar \((b)\) \(0.1\; {mm}\) \(4\; {cm}\) Thickness of bar \((d)\) \(0.01\; {mm}\) \(0.4 \;{cm}\) Depression \((\delta)\) \(0.01\; {mm}\) \(5 \;{mm}\) JEE Mains 2021 Hard