Explanation
Use formula of thermal expansion ,
ΔL=L0αΔT
where ΔL is the change in length of object after changing temperature
L0 is the initial length of object
ΔT is the temperature change
and α is the coefficient of linear expansion
Here, ΔL=5×10−5mm=5×10−8m
L0=1mm=10−3m
α=11×10−6C−1
Now, from formula,
5×10−8=10−3×11×10−6×ΔT
ΔT=5011
ΔT=4.5 C−1
Option C is correct.
Explanation:
∙In convection, transfer of heat took place by movement of gaseous and liquid molecules.
∙It generally happens in liquid and gas only where bulk portion is fluid. Sea and land breeze, trade wind and boiling water are example of such fluids. So, in those heat transfer is because of convection. But in bulb filament, resistance is responsible for transferring the heat which is example of conduction. So, in warming of glass bulb due to filament convection doesn’t take place.
Hence, option D is the correct answer.
In an experiment, 1.35 mol of oxygen (O2) are heated at constant pressure starting at 11.0ºC. How much heat must be added to the gas to double its volume?
For perfect gas,
Kinetic Energy of n molecule, K.E=n\left( \dfrac{1}{2}{{K}_{B}}T \right)
Where, {{K}_{B}} is Boltzmann constant
If there is no loss of energy.
Total kinetic energy of mixture is sum of each gas kinetic energy.
{{n}_{total}}K.{{E}_{total}}={{n}_{1}}K.{{E}_{1}}+{{n}_{2}}K.{{E}_{2}}+{{n}_{3}}K.{{E}_{3}}
\left( {{n}_{1}}+{{n}_{2}}+{{n}_{3}} \right)\left( \dfrac{1}{2}{{K}_{B}}T \right)={{n}_{1}}\left( \dfrac{1}{2}{{K}_{B}}{{T}_{1}} \right)+{{n}_{2}}\left( \dfrac{1}{2}{{K}_{B}}{{T}_{2}} \right)+{{n}_{3}}\left( \dfrac{1}{2}{{K}_{B}}{{T}_{3}} \right)
T=\dfrac{{{n}_{1}}{{T}_{1}}+{{n}_{2}}{{T}_{2}}+{{n}_{3}}{{T}_{3}}}{{{n}_{1}}+{{n}_{2}}+{{n}_{3}}}
From ideas gas equation
PV=nRT
PV=\dfrac{m}{{{M}_{o}}}RT
m=\dfrac{PV{{M}_{o}}}{RT}\
In first event
{{m}_{1}}=\dfrac{{{P}_{1}}V{{M}_{o}}}{R{{T}_{1}}}
6\ gram=\dfrac{PV{{M}_{o}}}{R\times 400}\
\dfrac{{{\operatorname{PVM}}_{o}}}{R}=400\times 6\ .\ .....\ (1)
In the second event when hole is made:
{{m}_{2}}=\dfrac{{{P}_{2}}V{{M}_{o}}}{R{{T}_{2}}}
{{m}_{2}}=\dfrac{\dfrac{P}{2}V{{M}_{o}}}{R\times 300}\ =\dfrac{1}{300\times 2}\dfrac{PV{{M}_{o}}}{R}
{{m}_{2}}=\dfrac{1}{300\times 2}\times \left( 400\times 6 \right)=4\ gram
Leak out oxygen is \left( 6gram-4\,gram \right)\ =\ 2\,gram
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