Q. 65.0( 1 Vote )

# Figure shows graphs of pressure vs density for an ideal gas at two temperatures T_{1} and T_{2}.

A. T_{1} > T_{2}

B. T_{1} = T_{2}

C. T_{1} < T_{2}

D. Any of three is possible

Answer :

From the graph, we can see that slope of straight line with temperature

T_{1} is greater than slope of straight line with temperature T_{2.}

Slope of straight line is given as:

Slope =

In our graph, slope is

where P=pressure

= density of gas

So, ratio for T_{1} is more than T_{2.}

Rms speed of gas is given as

where R=gas constant whose value is 8.31 J/mol K.

T=temperature of gas.

M= molar mass of molecule of gas

We also know that ideal gas equation is

PV=nRT

Where V= volume of gas

R=gas constant

T=temperature

N=number of moles of gas

So, we can write .

Putting the value of RT in equation (i),we get

nM= total mass of gas ‘m’

and density =

Putting the value of density in equation (ii)_{,} we get

Since ratio for T_{1} is more than T_{2} therefore rms speed for ideal gas at temperature T_{1} is more than temperature T_{2}. And if rms speed is more for temperature T_{1} then T_{1} > T_{2} from formula

v_{rms} =

Rate this question :

The condition of air in a closed room is described as follows. Temperature 25°C, relative humidity = 60%, pressure = 104 kPa. If all the water vapor is removed from the room without changing the temperature, what will be the new pressure? The saturation vapor pressure at 25°C = 3.2 kPa.

HC Verma - Concepts of Physics Part 2The weather report reads, “Temperature 20°C: Relative humidity 100%”. What is the dew point?

HC Verma - Concepts of Physics Part 2Pure water vapour is trapped in a vessel of volume 10 cm^{3}. The relative humidity is 40%. The vapour is compressed slowly and isothermally. Find the volume of the vapour at which it will start condensing.

The temperature and the dew point in an open room are 20°C and 10°C. If the room temperature drops to 15 °C, what will be the new dew point?

HC Verma - Concepts of Physics Part 2Find the number of molecules in 1 cm^{3} of an ideal gas at 0°C and at a pressure of 10^{–5} mm of mercury.

Consider a gas of neutrons. Do you expect it to behave much better as an ideal gas as compared to hydrogen gas at the same pressure and temperature?

HC Verma - Concepts of Physics Part 2