Two gases occupy two containers A and B the gas in A, of volume 0.10m³ , exerts a pressure of 1.40 MPa and that in B of volume 0.15m³ exerts a pressure 0.7 MPa. The two containers are united by a tube of negligible volume and the gases are allowed to intermingle. Then it the temperature remains constant, the final pressure in the container will be (in MPa)

To find the final pressure of the mixture when the two containers are connected, we can apply Boyle's Law or the principle of conservation of gas molecules (or moles) at a constant temperature.

According to the Ideal Gas Law:
$PV=nRT$

Since the temperature ($T$) remains constant and the gas constant ($R$) is a constant, the total number of moles ($n$) is directly proportional to the product of pressure ($P$) and volume ($V$). That is, $n=\frac{PV}{RT}$.

Let:
- For container A: volume $V_A=0.10{\text{m}}^3$, pressure $P_A=1.40\text{MPa}$
- For container B: volume $V_B=0.15{\text{m}}^3$, pressure $P_B=0.7\text{MPa}$

The total number of moles before mixing is the sum of the moles in both containers:
$n_{\text{total}}=n_A+n_B$

Substituting $n=\frac{PV}{RT}$ into the equation, we get:
$\frac{P_f{V}_f}{RT}=\frac{P_A{V}_A}{RT}+\frac{P_B{V}_B}{RT}$

Since temperature ($T$) is constant throughout, we can cancel $RT$ from both sides, leaving:
$P_f{V}_f=P_A{V}_A+P_B{V}_B$

Here, the final volume $V_f$ is the combined volume of both containers because the connecting tube has negligible volume:
$V_f=V_A+V_B=0.10{\text{m}}^3+0.15{\text{m}}^3=0.25{\text{m}}^3$

Now, solve for the final pressure $P_f$:
$P_f=\frac{P_A{V}_A+P_B{V}_B}{V_A+V_B}$

Substitute the given values into the equation:
$P_f=\frac{(1.40\text{MPa}\times 0.10{\text{m}}^3)+(0.7\text{MPa}\times 0.15{\text{m}}^3)}{0.25{\text{m}}^3}$

Calculate the products in the numerator:
- $1.40\times 0.10=0.14$
- $0.7\times 0.15=0.105$

Add the values in the numerator:
- $0.14+0.105=0.245$

Divide by the final volume to get $P_f$:
$P_f=\frac{0.245}{0.25}=0.98\text{MPa}$

Thus, the final pressure in the containers is 0.98 MPa.