The velocity of liquid coming out of a small hole of a large vessel containing two different liquids shown in figure is

Option 1 -

2√gh

Option 2 -

√2gh

Option 3 -

√gh

Option 4 -

3√gh

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A liquid of coefficient of cubical expansion $γ$ is filled in a container having coefficient of linear expansion $\frac{γ}{3} .$ On heating, liquid level in the container will

Vishal Baghel

$Δ V_{L} = V_{0 γ Δ T}$

$\Rightarrow Δ V_{s} = V_{0} \times 3 \times \frac{γ}{3} \times Δ T$

$\Rightarrow Δ V_{L} - Δ V_{S} = 0$

Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : When a rod lying freely is heated, no thermal stress is developed in it.

Reason R : On heating, the length of the rod increases.

In the light of the above statements, choose the correct answer from the options given below:

Vishal Baghel

Thermal stress is developed on heating when expansion of rod is hindered.

At what temperature a gold ring of diameter 6.230cm be heated so that it can be fitted on a wooden bangle of diameter. 6.241cm? Both the diameters have been measured at room temperature (27°C).

(Given : coefficient of linear thermal expansion of gold a_L = 1.4 × 10^-5 K^-1)

Vishal Baghel

According to question, we can write

$d = d_{0} (1 + α Δ T) \Rightarrow 6.241 = 6.230 (1 + 1.4 \times 1 0^{- 5} \times Δ T)$

$\Rightarrow T = 126.18 + 27 = 153.18 ° C$

A calorimeter consists of 400g of water at $24 ° C .$ A 500g piece of copper at $100 ° C$ is thrown into the water and the equilibrium temperature is found to be $36.5 ° C .$ What is the molar heat capacity of copper in cal/mol k, given that 1 mol of copper has a mass of 63.5g? Neglect the heat capacity of the container.

Vishal Baghel

400 × 1 × 12.5 = 500 × 5 × (100 – 36.5)

$S = \frac{10}{63.5} c a l / g m ° C$

$1 g m = \frac{1}{63.5} m o l$

S = 10 cal/mol °C

An igloo, a hemispherical enclosure built of ice $(1.67 J / m - s ° C)$ , has as inner radius of 2.50m. The thickness of the ice is 0.5m. At what rate must thermal energy be generated to maintain the air inside the igloo at $5 ° C$ when the outside temperature is - $40 ° C ?$ Ignore all thermal energy losses through the ground or by air currents.