Question

do it fast.............​

Answer 1

$\large\bf{\underline{\underline{\red{SOLUTION:-}}}}$

GIVEN :-

✫ A car tyre has air at 1.5 atm at 300K .

✫ Pressure increases to 1.75 atm at constant volume .

$\rm{P_{initial}\:=\:1.5\:atm}$

$\rm{P_{final}\:=\:1.75\:atm}$

$\rm{T_{initial}\:=\:300\:K}$

To Find :-

The temperature, i.e $\rm{T_{final}}$ .

FORMULA :-

✫ We have know that the ideal gas equation, i.e

$\bigstar\:\rm{\underline{\purple{\boxed{PV\:=\:nRT}}}}$

P = Pressure

V = Volume

R = Universal gas constant

T = Temperature

✪ Here, ‘n’ , ‘ R’ and ‘V’ are constant terms .

$\rm{\implies\:P\:=\:(\dfrac{nR}{V})\:T\:}$

✪ In the above equation, ( nR/V ) = constant = k .

$\rm{\implies\:P\:=\:kT}$

‘k’ is the constant term .

$\rm{\implies\:P\:\alpha\:T}$

$\bigstar\:\large\rm{\underline{\underline{\blue{\boxed{\dfrac{P_i}{P_f}\:=\:\dfrac{T_i}{T_f}\:}}}}}$

CALCULATION :-

$\rm{\implies\:T_f\:=\:\dfrac{P_f}{P_i}\:\times{T_i}\:}$

$\rm{\implies\:T_f\:=\:\dfrac{1.75}{1.5}\:\times{300}\:}$

$\rm{\green{\boxed{\implies\:T_f\:=\:350\:K\:}}}$

▼ Therefore, the temperature is 350K .

Answer 2

Given:

• Initial pressure of air in tyre,P₁= 1.5 atm

• Final pressure of air in tyre,P₂= 1.75 atm

• Initial temperature of air in tyre,T₁= 300 K

To Find:

• Final temperature of air

Solution:

According to equation of Ideal gas,

$\pink{\underline{\boxed{\bf{PV=nRT}}}}$

where,

• P is pressure

• V is volume

• n is no. of moles

• R is gas constant

• T is temperature

If volume, temperature and same amount of gas is taken then

$\purple{\underline{\boxed{\bf{\dfrac{P}{T}=constant}}}}$

or

$\orange{\underline{\boxed{\bf{\dfrac{P_{1}}{T_{1}}=\dfrac{P_{2}}{T_{2}}}}}}$

where,

• P₁ initial pressure

• T₁ is initial temperature

• P₂ is final pressure

• T₂ is final temperature

━━━━━━━━━━━━━━━━━━━━━━━━━

Let the final temperature be T₂

So,

$\longrightarrow\rm{\dfrac{P_{1}}{T_{1}}=\dfrac{P_{2}}{T_{2}}}$

$\longrightarrow\rm{\dfrac{1.5}{300}=\dfrac{1.75}{T_{2}}}$

$\longrightarrow\rm{T_{2}=\dfrac{1.75\times300}{1.5}}$

$\longrightarrow\rm\green{T_{2}=350^{\circ}C}$

Hence, the final temperature is 350°C.