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The thermodynamic state of a closed system containing a pure fluid changes from (T 1 , p 1 ) to (T 2 , p 2 ) , where T and p denote the temperatur e and pressure, respectively. Let Q denote the heat absorbed ( > 0 if absorb1 AnswerWhat does denote in the relation0 AnswerA nalysis of a flow phenomenon in a system requires the following variables: i. Pressure [M L1 T 2] ii. Velocity of the fluid [L T 1] iii. Size of the system [L] iv. Density of the fluid [M L3] v. Viscosity of the fluid [M L1 T 1] According to Buckingham Pi theorem (dimensional analysis) what is the number of independent DIMENSIONLESS variables needed to describe this system?1 AnswerLet N denote the set of all non-negative integers and Z denote the set of all integers. The function f : Z → N given by f(x) = |x| is:0 AnswerLet D ⊂ R 2 denote the closed disc with center at the origin and radius 2. (gate 2018 engineering mathematics)0 AnswerL et G be a graph with 100! vertices, with each vertex labelled by a distinct permutation of the numbers 1,2, … , 100. There is an edge between vertices 𝑢 and 𝑣 if and only if the label of 𝑢 can be obtained by swapping two adjacent numbers in the label of 𝑣. Let 𝑦 denote the degree of a vertex in G, and 𝑧 denote the number of connected components in G. Then, 𝑦 + 10𝑧 = _____.1 AnswerThe contents of a well-insulated tank are heated by a resistor of 23Ω in which 10A current is flowing. -gate-mechanical-20111 AnswerThe amount of heat absorbed or given out depends on ( NIFT UG )1 AnswerWhat does happens when water is condensed into ice ?0 Answer1 kg of a liquid is converted into its vapour at its boiling point. The heat absorbed in the process is called—0 AnswerLet X denote R2 endowed with the usual topology. Let Y denote R endowed with the co-finite topology. If Z is the product topological space Y Y; then0 AnswerC onsider a fully developed, two-dimensional and steady flow of a viscous fluid between two fixed parallel plates separated by a distance of 30 mm. The dynamic viscosity of the fluid is 0.01 kg/m-s and the pressure drop per unit length is 300 Pa/m. The fluid velocity at a distance of 10 mm from the bottom plate, in m/s, is ________.0 AnswerIn a counter flow heat exchanger, hot fluid enters at 100°C and leaves at 50°C. Cold fluid enters at 30°C and leaves at 40°C. If heat losses are ignored, then the logarithmic mean temperature difference (LMTD) is ________ °C (round off to 1 decimal place).0 AnswerA gas turbine with air as the working fluid has an isentropic efficiency of 0.70 when operating at a pressure ratio of 3. Now, the pressure ratio of the turbine is increased to 5, while maintaining the same inlet conditions. Assume air as a perfect gas with specific heat ratio 1.4 . If the specific work output remains the same for both the cases, the isentropic efficiency of the turbine at the pressure ratio of 5 is ______ (round off to two decimal places)0 AnswerIn a cross-flow filtration process, the pressure drop (ΔP) driving the fluid flow is 2 atm, inlet feed pressure (Pi ) is 3 atm and filtrate pressure (Pf) is equal to atmospheric pressure.0 AnswerIn a process occurring in a closed system F , the heat transferred from F to the surroundings E is 600 J. If the temperature of E is 300 K and that of F is in the range 380 - 400 K , the entropy changes of the sur1 AnswerLet W(n) and A(n) denote respectively, the worst case and average case running time of an algorithm executed on an input of size n. Which of the following is ALWAYS TRUE? -gate-computer science-20121 AnswerIn a closed piston-cylinder system, methane was observed to obey the following equation of state P V nb nRT ( ) where b = 0.029 m3 /mol. The temperature and volume are 500 oC and 5 m3 respectively for 100 moles of methane. At this state of the system, the isobaric rate of change of temperature with volume (in oC/m3 ) is __________ (rounded off to second decimal place).0 AnswerThe elementary irreversible gas-phase reaction A → B + C is carried out adiabatically in an ideal CSTR (Continuous-Stirred Tank Reactor) operating at 10 atm. Pure A enters the CSTR at a flow rate of 10 mol/s and a temperature of 450 K. Assume A, B and C to be ideal gases. The specific heat capacity at constant pressure ( CPi ) and heat of formation 0 ( ) Hi , of component i (i = A, B, C), are:0 AnswerLet X be a random variable with characteristic function φX(⋅) such that φX(2 π) = 1. Let Z denote the set of integers. Then P(X ∈ Z) is equal to ...0 Answer