The spectral distribution of radiation from a black body at $T_1=3000 \: K$ has a maximum at wavelength $\lambda_{\text{max}}$. The body cools down to a temperature $T_2$. If the wavelength corresponding to the maximum of the spectral distribution at $T_2$ is $1.2$ times of the original wavelength $\lambda_{\text{max}}$, then the temperature $T_2$ is _________ $K$ (round off to nearest integer)

The heat loss from a fin is $6$ W. The effectiveness and efficiency of the fin are $3$ and $0.75$, respectively. The heat loss (in W) from the fin, keeping the entire fin surface at base temperature, is _______.

A steel bar is held by two fixed supports as shown in the figure and is subjected to an increase of temperature $\Delta T=100^{\circ}C$. If the coefficient of thermal expansion and Young's modulus of elasticity of steel are $11 \times 10^{-6}/^{\circ} C$ and $200$ GPa, respectively, the magnitude of thermal stress (in MPa) induced in the bar is _______

A metal ball of diameter $60$ mm is initially at $220^{\circ}$ C. The ball is suddenly cooled by an air jet of $20^{\circ}$ C. The heat transfer coefficient is $200 W/m^{2}.K$. The specific heat, thermal conductivity and density of the metal ball are $400$ J/kg.K, ... $^{\circ} C$) after $90$ seconds will be approximately $141$ $163$ $189$ $210$

In a counter-flow heat exchanger, water is heated at the rate of $1.5 \: kg/s$ from $40^{\circ}$ C to $80^{\circ} \: C$ by an oil entering at $120^{\circ}$ C and leaving at $60 ^{\circ}$ C. The specific heats of water and oil are $4.2 \: kJ/kg.K$ ... heat transfer coefficient is $400 W/m^{2}.K$. The required heat transfer surface area (in $m^{2}$) is $0.104$ $0.022$ $10.4$ $21.84$