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Thermal Properties of Matter Overview

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Thermal Properties of Matter Overview Class 11th

Two different wires having lengths $L_{1}$ $_{}$ and $_{}$ $L_{2}$ , and respective temperature coefficient of linear 4expansion $α_{1}$ $_{}$ and $α_{2}$ $_{}$ , are joined end-to-end. Then the effective temperature coefficient of linear expansion is:

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Vishal Baghel

Contributor-Level 10

At T°C L = L? + L?
At T +? T Leq = L'? + L'?
where L'? = L? (1 + α? T)
L'? = L? (1 + α? T)
Leq = (L? + L? ) (1 + αavg? T)

⇒ (L? + L? ) (1 + αavg? T) = L? + L? + L? α? T + L? α? T
⇒ (L? + L? )αavg = L? α? + L? α?
⇒ αavg = (L? α? + L? α? )/ (L? + L? )

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Thermal Properties of Matter Overview Class 11th

Two different metal bodies A and B of equal mass are heated at a uniform rate under similar conditions. The variation of temperature of the bodies is graphically represented as shown in the figure. The ratio of specific heat capacities is :
(The graph shows Temperature (°C) on the y-axis and Time (s) on the x-axis. Both A and B are straight lines starting from the origin. For body A, temperature reaches 120°C in 4s. For body B, temperature reaches 90°C in 6s.)

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Raj Pandey

Contributor-Level 9

dQA = mACA dTA
dQB = mBCB dTB
dQA/dt = dQB/dt
⇒ mACA (dTA/dt) = mBCB (dTB/dt)
⇒ (dTA/dt)/ (dTB/dt) = (mBCB)/ (mACA)
Assuming mA = mB
(dTA/dt)/ (dTB/dt) = CB/CA
CA/CB = (dTB/dt)/ (dTA/dt) = (90/6)/ (120/3) = 15/40 = 3/8

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Thermal Properties of Matter Overview Class 11th

A steel rod with y = 2.0 * 10¹¹ Nm^-2 and a = 10^-5 °C^-1 of length 4m and area of cross-section 10cm² is heated from 0°C to 400°C without being allowed to extend. The tension produced in the rod is x * 10⁵ N where the value of x is_________.

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alok kumar singh

Contributor-Level 10

Force = Aya $Δ T$

Force $= (10 * 1 0^{- 4}) * (2 * 1 0^{11}) * 1 0^{- 5} * 400$

$F = 8 * 1 0^{5} N$

$x * 1 0^{5} = 8 * 1 0^{5}$

x = 8

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Thermal Properties of Matter Overview Class 11th

Consider two separate ideal gases of electrons and protons having same number of particles. The temperature of both the gases are same. The ratio of the uncertainty in determining the position of an electron to that of a proton is proportional to:-

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Vishal Baghel

Contributor-Level 10

Heisenberg uncertainty principle :

$\begin{array}{l} \Rightarrow Δ x Δ p \geq ? \\ \Rightarrow Δ x (m Δ v) \geq ? \end{array}$

$\Rightarrow Δ x (m \sqrt[]{\frac{3 R T}{m}}) \geq ?$

$\Rightarrow Δ x \propto \frac{1}{\sqrt[]{m}}$

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Thermal Properties of Matter Overview Class 11th

A rod CD of thermal resistance 10.0 KW^-¹ is joined at the middle of an identical rod AB as shown in figure. The end A, B and D are maintained at 200°C, 100°C and 125°C respectively. The heat current in CD in P watt. The value of P is……. .

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Vishal Baghel

Contributor-Level 10

$\Rightarrow H_{1} = H_{2} + H_{3}$

$\frac{200 - T}{5} = \frac{T - 125}{10} + \frac{T - 100}{5}$

$\Rightarrow T = 145 ° C \Rightarrow H_{2} = \frac{145 - 125}{10} = 2 W$

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Thermal Properties of Matter Overview Class 11th

For an ideal gas PT³ = constant. Find the coefficient of volume expansion of the gas is:

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Vishal Baghel

Contributor-Level 10

PT³ = k (constant)

$\Rightarrow (\frac{n R T}{V}) T^{3} = k$

$\Rightarrow T^{4} V^{- 1} = k$

$\Rightarrow T^{4} = k V$

$\Rightarrow 4 * \frac{Δ T}{T} = \frac{Δ V}{V}$ - (i) >

$\Rightarrow Δ V = V Y Δ T$ - (ii) >

Comparing I > & ii >

$\Rightarrow Y = \frac{4}{T}$

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Thermal Properties of Matter Overview Class 11th

A balloon carries a total load of 185 kg of normal pressure and temperature of 27°C. What load with the balloon carry on rising to a height at which the barometer pressure is 45cm of Hg and the temperature.

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Vishal Baghel

Contributor-Level 10

$P = ρ R T$

$\Rightarrow \frac{ρ_{1}}{ρ_{2}} = \frac{P_{1}}{P_{2}} * \frac{T_{2}}{T_{1}} = \frac{76}{45} * \frac{260}{300}$

$\Rightarrow \frac{ρ_{1}}{ρ_{2}} = \frac{M_{1}}{M_{2}}$

$\Rightarrow M_{2} = \frac{45 * 300 * 185}{76 * 266} = 123.54 k g$

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2 months ago

Thermal Properties of Matter Overview Class 11th

The temperature of equals masses of three different liquids x, y and z are 10°C, 20°C and 30°C respectively. The temperature of mixture when x is mixed with y is 16°C and that when y is mixed with z is 26°C. Temperature of mixture when x and z are mixed will be:

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alok kumar singh

Contributor-Level 10

ms_x (16 – 10) = ms_y (20 – 16)

$\Rightarrow \frac{s_{x}}{s_{y}} = \frac{2}{3}$

$m s_{y} (26 - 20) = m s_{z} (30 - 26)$

$\Rightarrow \frac{s_{y}}{s_{z}} = \frac{2}{3}$

$\frac{s_{x}}{s_{z}} = \frac{s_{x}}{s_{y}} * \frac{s_{y}}{s_{z}} = \frac{2}{3} * \frac{2}{3} = \frac{4}{9}$

$m s_{x} (T - 10) = m s_{z} (30 - T)$

->4(T – 10) = 9(30 – T)

->T = 23.84°C

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2 months ago

Thermal Properties of Matter Overview Class 11th

Read the following statements:

(A) When small temperature difference between a liquid and its surrounding is doubled, the rate of loss of heat of the liquid becomes twice.

(B) Two bodies P and Q having equal surface areas are maintained at temperature 10°C and 20°C. The thermal radiation emitted in a given time by P and Q are in the ratio 1:1. 15.

(C) A Carnot Engine working between 100K and 400K has an efficiency of 75%.

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